I think the heart and other body parts just gradually wear out and finally something stops working that you can't live without, so you die. Also, I have included the answer to another question that has already been asked to help you with your question!

Q: What are the reasons that could keep humans from living longer
than anyone does now?

A: Scientists are very interested in your question. They're studying what causes our cells to die. Their name for cell death is 'apoptosis.' You could search for that on www.google.com. A big question in science is whether we could live to be very old if we learned how to control the things that kill our cells. There's also some interesting research on why people and animals seem to sometimes live longer if they don't eat very much. There seems to be a vitamin that we use for digesting food that can also protect our cells from dying, but if all gets used up in digesting our food, there's not so much for keeping our cells alive. This research is very new, so it may turn out to be much more complicated than that, but it is quite exciting.

I sort of answered this question in my answer to question: (Do cells go through the same changes as human beings, or do they go through different changes? In other words, do they start little, go through some kind of puberty, then get old??Search Scienceline for key words: cell and age) , so please read that answer. In short, yes, people do just die of old age, but some people live a lot longer than others and why that is, we do not know.